F=m.a, this one will give us the force in Newtons.
Weight=m.g, this one will give us a force in terms of kg x g. We call this as kgf when we don't multiply and put the 'g' while mentioning the value. Eg: say for 60kg of body lying on the table, its weight(force) will be 60x9.8=588 Newtons. But, we can mention it as 60kgf.
Newton= kg x g = kg x 9.8
let understand in short term
KGF is known as kilogram-force
where 1kgf = 9.8N
example 10 KGF = 10 x 9.8 N = 98 N